A method of the foregoing general type has been disclosed in printed German patent specification DE-A No. 26 60 068. While this known method makes it possible to abstract admittedly large quantities of water from the air that will well be sufficient for large-scale irrigation efforts even while utilizing a difference in elevations to generate hydroelectric energy for self-sufficiency of the system operating on said method, the water yield will still be limited by the fact that the supply of heat required for the expulsion of moisture in every second phase of the process cycle cannot be improved beyond that permitted by the limited amount of solar radiation available.